this is the graph of a function. choose the graph of its derivative from among the following functions.
this is the graph of a function. choose the graph of its derivative from among the following functions.
Answer
Explanation:
Step1: Analyze slope of original function
The original function is decreasing on the left - hand side of its minimum point and increasing on the right - hand side. The derivative of a function is negative when the function is decreasing and positive when the function is increasing. Also, the derivative is zero at the minimum point of the original function.
Step2: Match with derivative graphs
We look for a graph of the derivative that is negative for small (x) values, crosses the (x) - axis (where the derivative is zero) at the (x) - value corresponding to the minimum of the original function, and is positive for larger (x) values.
Answer:
The graph of the derivative that has a negative (y) - value for small (x), crosses the (x) - axis at the appropriate (x) - value and has a positive (y) - value for larger (x) values is the correct one. Without specific labels on the graphs, we can't point out exactly which one among the given options it is, but the correct graph of the derivative will have these characteristics: negative slope for (x) values where the original function is decreasing, zero at the minimum of the original function, and positive slope for (x) values where the original function is increasing.